Proof Number-Based Monte Carlo Tree Search

Abstract

In this article, we proposes a new game-search algorithm, PN-Monte Carlo tree search (MCTS), which combines MCTS and proof-number search (PNS). These two algorithms have been successfully applied for decision making in a range of domains. We define three areas where the additional knowledge provided by the proof and disproof numbers gathered in MCTS trees might be used: final move selection, solving subtrees, and the UCB1 selection mechanism. We test all possible combinations on different time settings, playing against vanilla Upper Confidence bounds applied to Trees on several games: Lines of Action (7 × 7 and 8 × 8 board sizes), MiniShogi, Knightthrough, and Awari. Furthermore, we extend this new algorithm to properly address games with draws, like Awari, by adding an additional layer of PNS on top of the MCTS tree. The experiments show that PN-MCTS is able to outperform MCTS in all tested game domains, achieving win rates up to 96.2% for Lines of Action.